Introduction to Computer Networks - bit-netlab.org · Assign sequence numbers to outgoing frames, so that the receiver can distinguish proper retransmissions ... Generator polynomial

Introduction to Computer Networks

Tian Song (嵩天), Ph.D., Assoc. [email protected]

Introduction to Computer Networks

Tian Song (嵩天), Ph.D., Assoc. [email protected]

Design Issue and Error Correction

School of Computer Science and Technology, BIT, http://cs.bit.edu.cn/~songtian3

Outline

• Design of Data Link Layer

• Framing

• Error Correction

• Example: PPP


Data Link LayerBasic Services:

–Network layer passes a number of bits (frame) to the data link layer.

– Data link layer is responsible for transmitting the frame to the destination machine.

– Receiving layer passes received frame to its network layer.


Data Link Layer• Data link layer is responsible to transmit bits from source to destination

• Three jobs: framing, error control, and flow control(a) Virtual communication. (b) Actual communication.


Data Link LayerDuty:

Transmit a set of 0 and 1 without error

Question:

How a data frame can be reliably transmit?

How a shared channel can be accessed?


Framing

Question:

How to encapsulate a bit stream into frames?

(1) Character count

(2) Flag byte


Framing: Character Count

A character stream. (a) Without errors. (b) With one error.


Framing: Flag ByteMark the beginning and end of a frame with a flag byte

Byte stuffing


Framing: Flag ByteMark the beginning and end of a frame with a 01111110

For a given sequence (a), then…

bit stuffing


FramingThinking about byte stuffing and bit stuffing:

Pros:practical way to frame a bit streaming

Cons:the length of frames depend on the original bits


Error Correction

Question:

How to detect or correct transfer errors of frames?

发现纠正

What kind of errors there are in the transmission?

(1) frame lost

(2) bit error (error in flags, error in content)


Frame LostHow to solve “frame lost”?

Acknowledgement:

Receiver sends back to sender special control frames

Timer:

Sender starts a timer to detect acknowledge frame

Sequencing:

Assign sequence numbers to outgoing frames, so that

the receiver can distinguish proper retransmissions


Frame LostWhy there is “frame lost”?

Unmatched Rate:

Fast sender will flood the slow receiver.

Two Solutions:

(1) feedback‐based flow control:

the receiver tells the sender how to send.

(2) rate‐based flow control:

protocol has a way to limit the senders’ rate.


Bit ErrorRedundant information is the key! (m+r)

Two Philosophies

More redundant information : So, receivers can correct some errors.

Less redundant information:

So, receivers can detect errors and

ask retransmission if there are errors.


Error Correcting CodesHamming Code:

Hamming distance is the number of differences

between two frames a and b at the same position.

E.g. the distance (d) is _______.


Error Correcting CodesHamming Code:

Coding schema (编码方案) example:

00000 00000

00000 11111

11111 00000

11111 11111

Only 4 codes exist.

The distance of coding schema is _________.

If we receive:

00000 00011

00000 00111


Error Correcting CodesHamming Codes: To correct 1 bit error:

p1=(p1, m3, m5, m7, m9, m11)

p2=(p2, m3, m6, m7, m10, m11)

p4 =(p4, m5, m6, m7)

p8 =(p8, m9, m10, m11)

() : 偶校验


Error Correcting CodesTo correct 1 bit error:

p1=(p1, m3, m5, m7, m9, m11)

p2=(p2, m3, m6, m7, m10, m11)

p4 =(p4, m5, m6, m7)

p8 =(p8, m9, m10, m11)


Error Detecting CodesParity: (奇偶校验)

One parity bit

The parity bit is chosen so that the number of 1 bits

in the codeword is even (or odd)

1011100__ , for odd parity, what ‘s the bit? 1


Error Detecting CodesParity is too simple, it can only detect one bit error.

Question:

How to detect k‐bit errors?

CRC: (循环冗余校验码)

Cyclic Redundancy Check

IEEE standard


Error Detecting CodesCRC: (循环冗余校验码)

Treats bit strings as representations with coefficients

of 0 and 1 only.

E.g. Bit string 110001, as x5 + x4 + x0

also as 1x5 + 1x4 + 0x3 + 0x2 + 0x1 + 1x0

Then, the operations of two strings is XOR.



Generator polynomial (生成多项式): G(x)

• both the high‐ and low‐ order bits

• G(x) as divisor

So, the idea of CRC is

add some checksum to the string, so the new string

can divide G(x) without reminder.


Error Detecting Codes



r‐bit checksum can detect <= r‐bit errors.

E.g. G(x) = 10011, the max detect error is _____?

CRC‐12 =x12+x11+x3+x2+x1+1

CRC‐16 =x16+x15+x2+1

CRC‐CCITT =x16+x12+x5+1

CRC‐32 (The max detect error of CRC‐32 is _____?)


Example: PPPPPP: (Point to Point Protocol)

used in SONET and ADSL

Today, we observe framing and error correction.


Example: PPPPPP Framing

flag byte: 01111110 (0x7E)

how about the stuffing?


Example: PPPPPP Framing

Byte stuffing with 0x7D and XOR 0x20


Example: PPPPPP Error Correction:

No error correction, but error detection.

2‐byte or 4‐byte checksum.

CRC‐16, CRC‐32


Conclusion

• Design Issue of Data Link Layer

• Framing

• Error Correction

• Example: PPP


End

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Introduction to Computer Networks - bit-netlab.org · Assign sequence numbers to outgoing frames, so that the receiver can distinguish proper retransmissions ... Generator polynomial